In applied mathematics, the reflecting function
of a differential system
connects the past state
of the system with the future state
of the system by the formula
The concept of the reflecting function was introduced by Uladzimir Ivanavich Mironenka.
with the general solution
in Cauchy form, the Reflecting Function of the system is defined by the formula
transformation (Poincaré map) of the differential system
Therefore the knowledge of the Reflecting Function give us the opportunity to find out the initial dates
of periodic solutions of the differential system
and investigate the stability of those solutions.
For the Reflecting Function
the basic relation is holding.
Therefore we have an opportunity sometimes to find Poincaré map of the non-integrable in quadrature systems even in elementary functions.